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Question
Find the equation of the line passing through the point of intersection of 7x + 6y = 71 and 5x – 8y = −23; and perpendicular to the line 4x – 2y = 1.
Solution
7x + 6y = 71 `=>` 28x + 24 = 284 ...(1)
5x − 8y = −23 `=>` 15x − 24y = −69 ...(2)
Adding (1) and (2), we get,
43x = 215
x = 5
From (2),
8y = 5x + 23
= 25 + 23
= 48
`=>` y = 6
Thus, the required line passes through the point (5, 6).
4x − 2y = 1
2y = 4x − 1
`y = 2x - 1/2`
Slope of this line = 2
Slope of the required line =`(-1)/2`
The required equation of the line is
y – y1 = m(x1,x2)
`y - 6 = (-1)/2 (x - 5)`
2y − 12 = −x + 5
x + 2y = 17
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